If set A is a subset of B we say that all elements in A can be found.pdf

If set A is a subset of B we say that all elements in A can be found in B. If P(B) > 0, what is the
value of P(A|B)?
Solution
HERE GIVEN THAT THE SET A IS SUBSET OF B
HENCE ALL ELEMENT OF A WILL BE IN B
ALSO (A INTERSECTION B) = SET A
NOW P(A|B) = P(A INTERSECTION B) / P(B)
= P(A)/P(B) [ AS P( A INTERSECTION B ) = P(B)]
HENCE THE VALUE OF P(A)/P(B) <1.

1. If set A is a subset of B we say that all elements in A can be found in B. If P(B) > 0, what is the
value of P(A|B)?

Solution

HERE GIVEN THAT THE SET A IS SUBSET OF B
HENCE ALL ELEMENT OF A WILL BE IN B
ALSO (A INTERSECTION B) = SET A
NOW P(A|B) = P(A INTERSECTION B) / P(B)
= P(A)/P(B) [ AS P( A INTERSECTION B ) = P(B)]
HENCE THE VALUE OF P(A)/P(B) <1